3. At this point, you can go back to Trello and try to use the GitHub button to attach something. This will ask you to reauthenticate with GitHub. During the authorization flow you will see a screen that looks like the screenshot below:

On this page, make sure that the organization has a green checkmark next to it (like the Trello org in this screenshot). If it doesn't, you may need to reach out to your organization's admins to change its settings. It may be that the organization has third party application restrictions on it. See https://help.github.com/articles/about-third-party-application-restrictions/ for more information.